Abstract Geometry
The ancient Egyptians and Babylonians discovered abstract Geometry. They developed these ideas that were used to build pyramids and help with reestablishing land boundaries. While, the Babylonians used abstract geometry for measuring, construction buildings, and surveying. Abstract geometry uses postulates, rules, definitions and propositions before and up to the time of the Euclid.
Abstract geometry is deductive reasoning and axiomatic organization. Deductive reasoning deals with statements that have already been accepted. An example of deductive reasoning is proving the sum of the measures of the angles of a quadrilateral is 360 degrees. Another example of deductive reasoning is proving the sum of the angles of a trigon is equal to 180 degrees. From this we get, any quadrilateral can be divided into two trigons. Axioms, which are also called postulates, are statements that can be proved true by using deductive reasoning.
Measurement geometry contains theories that exist and can have supporting ideas to back them up, and cannot be disproved. Hyperbolic geometry and elliptic geometry are two examples of measurement geometry. Non-Euclidean geometry can be considered measurement geometry, since it is a branch in which the fifth postulate of Euclidean Geometry is replaced by one of the two alternative postulates. Mathematicians in the nineteenth century showed that it is possible to create consistent geometries with Euclid's postulates.
An example of the difference in the abstract geometry and the measurement geometry is the sum of the measures of the angles of a trigon. The sum of the measures of the angles of a trigon is 180 degrees in Euclidian geometry, less than 180 in hyperbolic, and more than 180 in elliptic geometry. The area of a trigon in hyperbolic geometry is proportional to the excess of its angle sum over 180 degrees. In Euclidean geometry all trigons have an angle sum of 180 without respect to its area. Which means similar trigons with different areas can exist in Euclidean geometry. It is not possible in hyperbolic or elliptic geometry. In two-dimensional geometries, lines that are perpendicular to the same given line are parallel in abstract geometry, are neither parallel nor intersecting in hyperbolic geometry, and intersect at the pole of the given line in elliptic geometry. The appearance of the lines as straight or curved depends on the postulates for the space.
At the present time mathematics is trying to figure out which of the three is the best representation of the universe.
After 3rd century BC, Eratosthenes calculation about Earth's circumference was used correctly in different locations such as Alexandria and syene (Aswan now) by simple geometry and the shadows cast. Eratosthenes's results undertaken in 1ST century by Posidonius, were corroborated in Alexandria and Rhodes by the comparison between remarks is excellent.
That the world is, is apparent, but what the world is, is neither evident, nor easy to comprehend. The theoretical analysis of the universe has still been the hardest problem for metaphysics the object of which is to determine the nature of things and relations and to discover the ultimate principle ordering all things and changes into one world.
A triangle has certain properties such as all of the angles. add up to 180o and even if we have never thought about it before we clearly recognise these properties ‘whether we want to or not’. Cottingham. J. 1986). The 'Secondary' of the 'Se A triangle’s real meaning is independent of our mind, just as God’s existence is.
Geometry, a cornerstone in modern civilization, also had its beginnings in Ancient Greece. Euclid, a mathematician, formed many geometric proofs and theories [Document 5]. He also came to one of the most significant discoveries of math, Pi. This number showed the ratio between the diameter and circumference of a circle.
An underlying theme present throughout the series is the possibility that our existence is not the only one. According to current theories in physics, it is entirely possible that our universe is just one of many universes f...
Architectural designs changed greatly since the ancient times. Most famous architectures and sculptures today originated from the Greek and Roman civilizations. Moreover, some of the inventions from those civilizations are also being used today, such as the arch, which originated from Roman architecture, and the columns, which originated from the Greek architecture. Throughout history, these architectures and inventions have become the foundations for our buildings, churches, and much more.
Arches were used by Egyptians, Babylonians and Greeks, but they were rather small in size, and therefore not used as parts of large constructions like palaces. The Romans invented concrete, which allowed them to create arches that could support huge amounts
Euclidean distance was proposed by Greek mathematician Euclid of Alexandria. In mathematics, the Euclidean distance or Euclidean metric is the distance between two points, which is shown as a length of a line segment and is given by the Pythagorean theorem. The formula of Euclidean distance is a squ...
"The Foundations of Geometry: From Thales to Euclid." Science and Its Times. Ed. Neil Schlager and Josh Lauer. Vol. 1. Detroit: Gale, 2001. Gale Power Search. Web. 20 Dec. 2013.
Euclid, who lived from about 330 B.C.E. to 260 B.C.E., is often referred to as the Father of Geometry. Very little is known about his life or exact place of birth, other than the fact that he taught mathematics at the Alexandria library in Alexandria, Egypt during the reign of Ptolemy I. He also wrote many books based on mathematical knowledge, such as Elements, which is regarded as one of the greatest mathematical/geometrical encyclopedias of all time, only being outsold by the Bible.
But a circle was different, it could not be simply divided into length and width, for it had no sides. As it turns out, finding the measurement to be squared was not difficult as it was the radius of the circle. There was another aspect of the circle though that has led to one of the greatest mathematical voyages ever launched, the search for Pi. One of the first ever documented estimates for the area of a circle was found in Egypt on a paper known as the Rhind Papyrus around the time of 1650 BCE. The paper itself was a copy of an older “book” written between 2000 and 1800 BCE and some of the information contained in that writing might have been handed down by Imhotep, the man who supervised the building of the pyramids.
The Greeks made a revolutionary contribution to the architectural history, ancient Greek architects strived for precision, perspective and proportions. Newly invented mathematical formulas made the impossible possible, provided the basis for building resplendent architectural pieces with optical, spatial refinements, orders and meticulously crafted sculptures. The audacious approach expanded the conceptual boundary in architecture. Eventually, derivation of these audacious attempts influenced the architecture up till present, their excellence shall never be forgotten.
Trigonometry is one of the branches of mathematical and geometrical reasoning that studies the triangles, particularly right triangles The scientific applications of the concepts are trigonometry in the subject math we study the surface of little daily life application. The trigonometry will relate to daily life activities. Let’s explore areas this science finds use in our daily activities and how we use to resolve the problem.
Trigonometry (from Greek trigōnon "triangle" + metron "measure"[1]) is a branch of mathematics that studies triangles and the relationships between the lengths of their sides and the angles between those sides. Trigonometry defines the trigonometric functions, which describe those relationships and have applicability to cyclicalphenomena, such as waves. The field evolved during the third century BC as a branch of geometry used extensively for astronomical studies.[2] It is also the foundation of the practical art of surveying.
There is a triangle called the Heronian triangle. It has area and side lengths that are all integers. The Heronian triangle is named after the great hero of Alexandria. The term is sometimes applied more widely to triangles whose sides and area are all rational numbers. An Isosceles triangle is a triangle that has two sides of equal length. Sometimes is specified as having two and only two sides of equal length. Triangles are polygons with the least possible number of sides, which is